$\int x^{^{\frac15}}\,dx=$ $+C$
Explanation: The integrand is of the form $x^n$ where $n\neq-1$, so we can use the reverse power rule: $\int x^n\,dx=\dfrac{x^{n+1}}{n+1}+C$ $\begin{aligned} \int x^{^{{\frac15}}}\,dx&=\dfrac{x^{^{{\frac15}+1}}}{{\dfrac15}+1}+C \\\\ &=\dfrac56x^{^{\frac65}}+C \end{aligned}$ In conclusion, $\int x^{^{\frac15}}\,dx=\dfrac56x^{^{\frac65}}+C$